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Approximation Theory

From Taylor Polynomials to Wavelets

  • Textbook
  • © 2005

Overview

Authors:
  1. Ole Christensen

    1. Department of Mathematics, Technical University of Denmark, Lyngby, Denmark

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  2. Khadija L. Christensen

    1. Department of Mathematics, Technical University of Denmark, Lyngby, Denmark

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    You can also search for this author in PubMed   Google Scholar

  • Concisely written, user-friendly book
  • Demonstrates the dynamic nature of mathematics and the influence of classical disciplines on many areas of modern mathematics and applications
  • Includes classical, illustrative examples and constructions, exercises, and a discussion of the role of wavelets to areas such as digital signal processing and data compression
  • Includes supplementary material: sn.pub/extras

Part of the book series: Applied and Numerical Harmonic Analysis (ANHA)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Approximation with Polynomials

    • Ole Christensen, Khadija L. Christensen
    Pages 1-14

  3. Infinite Series

    • Ole Christensen, Khadija L. Christensen
    Pages 15-50

  4. Fourier Analysis

    • Ole Christensen, Khadija L. Christensen
    Pages 51-82

  5. Wavelets and Applications

    • Ole Christensen, Khadija L. Christensen
    Pages 83-104

  6. Wavelets and their Mathematical Properties

    • Ole Christensen, Khadija L. Christensen
    Pages 105-136

  7. Back Matter

    Pages 137-156
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Keywords

About this book

This book gives an elementary introduction to a classical area of mathemat­ ics - approximation theory - in a way that naturally leads to the modern field of wavelets. The main thread throughout the book is the idea of ap­ proximating "complicated expressions" with "simpler expressions," and how this plays a decisive role in many areas of modern mathematics and its applications. One of the main goals of the presentation is to make it clear to the reader that mathematics is a subject in a state of continuous evolution. This fact is usually difficult to explain to students at or near their second year of uni­ versity. Often, teachers do not have adequate elementary material to give to students as motivation and encouragement for their further studies. The present book will be of use in this context because the exposition demon­ strates the dynamic nature of mathematics and how classical disciplines influence many areas of modern mathematics and applications. The book may lead readers toward more advanced literature, such as the other pub­ lications in the Applied and Numerical Harmonic Analysis series (ANHA), by introducing ideas presented in several of those books in an elementary context. The focus here is on ideas rather than on technical details, and the book is not primarily meant to be a textbook.

Reviews

"Approximation methods and wavelets have found many important applications in signal processing. This well-written textbook provides an elementary introduction to approximation theory. The authors concentrate on the presentation of main ideas and demonstrate the great influence of classical approximation theory on modern applied mathematics. This book, with many illustrative examples, is easy to read…[and] will be very useful for anyone interested in approximation theory and wavelets."   —Zentralblatt Math

Authors and Affiliations

  • Department of Mathematics, Technical University of Denmark, Lyngby, Denmark

    Ole Christensen, Khadija L. Christensen

About the authors

Ole Christensen is the author of An Introduction to Frames and Riesz Bases (0-8176-4295-1).

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